Energy Approach for Determine Frequency and Amplitude of Vibration of Piping With Closed Side Branches

This article suggests calculation method for frequency and amplitude of acoustic vibration in piping with closed side branches, caused by gaseous running flow. The calculation algorithm consists of following steps: i) local excitation system is defined; ii) different combinations of boundary conditions are formed; iii) for fixed pair of boundary conditions ratio of stored in system energy and radiated from boundaries energy is written; iv) for every frequency energy functional is maximized to find boundary conditions; v) resonance frequencies are determined from plotting a curve of maximal energy ratio vs. frequency. Energy approach was further developed to analyze amplitude of vibration. For amplitude determine balance between injected energy (which depends on the Strouhal number and is defined from experimental data for laboratory geometries), and radiated from boundaries energy is written.